Answer:
(-1, -1)
Step-by-step explanation:
[tex]\boxed{midpoint=(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1}+y_{2} }{2}) }[/tex]
Midpoint of line segment
[tex]= (\frac{1-3}{2},\frac{-6+4}{2} )\\= (\frac{-2}{2},\frac{-2}{2})\\= (-1, -1)[/tex]
simplify each of the following exponential expressions:
a.
[tex] {7}^{2} [/tex]
b.
[tex] {6}^{3} [/tex]
c.
[tex] {12}^{2} [/tex]
d.
[tex] {2}^{4} [/tex]
e.
[tex] {10}^{3} [/tex]
Answer:
the answer is A
Step-by-step explanation:
Determine the equivalent system for the given system of equations:
2x + 3y = 7
4x – 2y = 4
A.2x + 3y = 7
8x – 4y = 4
B.2x + 3y = 7
6x + y = 11
C.-2x – 3y = 7
4x - 2y = 4
D.2x + 3y = 7
6x + y = 4
Answer:
[tex]\large\boxed{B.\ \left\{\begin{array}{ccc}2x+3y=7\\6x+y=11\end{array}\right}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+3y=7&(1)\\4x-2y=4&(2)\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+3y=7\\4x-2y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad6x+y=11\qquad(3)\\\\\text{Make the system of equation with (1) and (3):}\\\\\left\{\begin{array}{ccc}2x+3y=7\\6x+y=11\end{array}\right[/tex]
The equivalent system of equations for the given system of equations is
option (B)
[tex]2x+3y=7\\6x+y=11[/tex]
This is obtained by adding the given equations.
Equivalent system of equations:Systems of equations that have the same solution are called equivalent systems. Given a system of two equations, we can produce an equivalent system by replacing one equation with the sum of the two equations, or by replacing an equation with a multiple of itself.Calculating the equivalent system for the given system of equations:Given the system of equations as
[tex]2x+3y=7\\4x-2y=4[/tex]
Adding the two equations,
[tex]2x+3y+4x-2y=7+4\\6x+y=11[/tex]
Therefore, the system of equations
[tex]2x+3y=7\\6x+y=11[/tex]
are equivalent to the given set of equations.
Thus, option (B) is correct.
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Order these numbers from least to greatest.
3/4, -1/5, -5/16, 0.90, -0.52
0.90,34 , -5/16, -0.52, -1/5
-1/5, -5/16, -0.52, 3/4, 0.90
0.90, 3/4, -0.52, -5/16, -1/5
-0.52, -5/16, -1/5, ,3/4 0.90
The numbers ordered from least to greatest are -0.52, -5/16, -1/5, 3/4, and 0.90. Negative values are ordered by ascending absolute value, while positive values are ordered normally.
Explanation:To order the numbers from least to greatest, we first need to compare the negative numbers, then the positive fractions and decimals. It's important to understand that negative numbers are less than zero, and the number with the largest absolute value is actually the smallest when negative. Positive numbers are greater than zero, with larger decimal or fractional values representing larger numbers.
-0.52 (because it is the only number less than -0.5)-5/16 (which is equal to -0.3125, so it's greater than -0.52 but still negative)-1/5 (or -0.2, which is the largest of the negative numbers)3/4 (equal to 0.75 and is less than 0.90)0.90 (as it is the greatest positive decimal given)The correct order from least to greatest is: -0.52, -5/16, -1/5, 3/4, and 0.90.
Which of the following does not have triangular faces?
A. Dodecahedron
B. Icosahedron
C. Octahedron
D. Tetrahedron
Answer:
Step-by-step explanation:
Answer "A"
Dodecahedron
Dodecahedron does not have triangular faces.
What is Dodecahedron?The dodecahedron is also known as pentagonal dodecahedron which is composed of 12 regular pentagonal faces, 30 edges, and 20 vertices.
A regular icosahedron is a 3D polyhedron having 20 triangular faces, 30 edges, and 12 vertices.
A regular octahedron has 8 triangular faces, 6 vertices, and 12 edges.
A tetrahedron has 4 triangular faces, 4 vertices, and 6 edges.
All of these 3 have triangular faces.
But Dodecahedron has 12 faces which are pentagonal in shape.
Therefore Dodecahedron does not have triangular faces.
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Bev earns $2 a week for taking out her neighbor’s trash cans. Complete the table of values. Then state the domain and range.
Number of Weeks | Money Earned
1 |
2 |
3 |
4 |
Answer with Step-by-step explanation:
Bev earns $2 a week for taking out her neighbor’s trash cans.
Number of Weeks Money Earned ($)
1 2
2 4
3 6
4 8
As we can see the domain is the number of weeks which is:
{1,2,3,4,...}
and Range is the money earned in dollars which is:
{2,4,6,8,...}
Out of the 21 students in Mrs. Clark's class, 5of the class are boys and of the class are girls. How many students in the
class are girls and how many are boys?
(SHOW WORK)
Answer:
There are 4 boys and 17 girls in the class.
Step-by-step explanation:
Out of 21 students in Mrs. Clark's class, 5th of the students are boys and rest are girls.
out of 21 every 5th student is boy, so total boys are = [tex]\frac{21}{5}[/tex]
= [tex]4\frac{1}{5}[/tex]
The whole number is 4, so the number of boys are 4.
The number of girls = 21 - 4 = 17 girls
There are 4 boys and 17 girls in the class.
A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equation:
P=0.005y^2−0.01y+121
gives a person's blood pressure, P, at age y years.
A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 48 years.
B.) If a person's systolic pressure is 133 mm Hg, what is their age (rounded to the nearest whole year)?
Answer:
a) 132.0 mmHg, b) 50 years old.
Step-by-step explanation:
a) Plug in 48 where you see the letter y and simplify, preferably with a calculator.
P = 0.005(48)^2 - 0.01(48) + 121
P = 132.04 mmHg, to the nearest tenth would be 132.0 mmHg
b) Plug in 133 for P and solve for y.
0.005y^2 - 0.01 + 121 = 133
To make it a little easier on myself -- and because I haven't practiced a diff. method in a while -- I simplified the equation to 0.005y^2 - 0.01y - 12 = 0 by subtracting 133 from both sides. I did that so that I can could then use the quadratic formula to solve.
Quadratic formula is y = (-b +/- √(b^2 - 4ac)) / 2
Now we plug in our given information, that new trinomial, to solve for y
[tex]y = \frac{0.01 +/- \sqrt{(0.01)^2 - 4(0.005)(-12)} }{2(.0.005)} \\y = \frac{0.01 +/- \sqrt{0.2401}}{0.01}[/tex]
[tex]y = \frac{0.01}{0.01} +/- \frac{\sqrt{0.2401}}{0.01} \\y = 1 +/- \frac{0.49}{0.01}\\y = 1+/- 49[/tex]
Because it is a trinomial, you are given two answers. You get y = 48 and y = 50. In order to find out which is right, you plug in and see which on yields 133 as the answer. Given the part a), I already know it's not 48. When I plug in 50, I get 133. Therefore, 50 years old is your answer.
The systolic pressure for a person who is 48 years old is approximately 132.0 mm Hg. If a person's systolic pressure is 133 mm Hg, their age is approximately 49 years when rounded to the nearest whole year.
A) Systolic Pressure Calculation for Age 48
To find the systolic pressure for a person who is 48 years old, we use the given equation:
P = 0.005y^2 - 0.01y + 121
Substitute y = 48 into the equation:
P = 0.005(48)^2 - 0.01(48) + 121 = 0.005(2304) - 0.48 + 121 = 11.52 - 0.48 + 121 = 11.04 + 121 = 132.04 mm Hg
To the nearest tenth, the systolic pressure is 132.0 mm Hg.
B) Age Calculation for Systolic Pressure of 133 mm Hg
To find the age when a person's systolic pressure is 133 mm Hg, we set P = 133 and solve for y:
0.005y^2 - 0.01y + 121 = 133 0.005y^2 - 0.01y - 12 = 0
Using the quadratic formula, y = [-b ± √(b^2 - 4ac)] / (2a), where:
a = 0.005,
b = -0.01, and
c = -12.
We find the positive root that makes physical sense for age:
y ≈ 48.9 years
The age rounded to the nearest whole year is 49 years.
jewels has 6.75 to ride the ferry around Connecticut m it will cost her 0.45 every time she rides. identify the dependent variable and independent variable in this scenario
the number of rides is the independent variable and the total cost is the dependent variable
the total cost is the independent variable and the number of rides is the dependent variable
the number of rides and the total cost are both independent variables
the number of rides and total cost are both dependent variables
Answer:
Dependent would be the number of times she rides because it would add up to how many times she could ride. 6.75= x(.45)
Step-by-step explanation:
In Jewels' ferry ride scenario, the independent variable is the number of rides taken, and the dependent variable is the total cost incurred based on the rides. This follows the general rule where the dependent variable's outcome is determined by the choice made in the independent variable.
Explanation:In the scenario described, Jewels has a certain amount of money to spend on ferry rides, and each ride costs a fixed amount. Here, the number of ferry rides she can take is the independent variable, as it can be chosen freely by Jewels. The total cost of the ferry rides is the dependent variable, as it depends on the number of rides she takes.
Therefore, the correct answer is that the number of rides is the independent variable and the total cost is the dependent variable.
As for the given reference information, in the vacation resort case, the number of hours the equipment is rented is the independent variable, and the total fee is the dependent variable. This is similar to Jewels' scenario because the basic principle in both instances is about the relationship between a variable you can control (number of rides or hours) and a variable that depends on this control (total cost or total fee).
For example, if Jewels decides to ride the ferry 5 times, the total cost would be 5 rides × $0.45 per ride = $2.25. This demonstrates how the dependent variable (total cost) changes in response to a change in the independent variable (number of rides).
(-b3+ 3b2 + 8) - (? - 5b2 - 9) = 5b3 + 8b2 + 17
? =
DONE
Answer with Step-by-step explanation:
Let ?=x
We have to find the value of x in:
[tex](-b^3+3b^2+8)-(x-5b^2-9)=5b^3+8b^2+17[/tex]
Adding [tex]b^3[/tex] on both sides, we get
[tex]-b^3+3b^2+8-x+5b^2+9+b^3=5b^3+8b^2+17+b^3[/tex]
[tex]3b^2+8-x+5b^2+9=5b^3+8b^2+17+b^3[/tex]
Combining the like terms on both side, we get
[tex]8b^2+17-x=6b^3+8b^2+17[/tex]
Subtracting both sides by 8b², we get
[tex]8b^2-x+17-8b^2=6b^3+8b^2+17-8b^2[/tex]
[tex]-x+17=6b^3+17[/tex]
subtracting both sides by 17, we get
[tex]-x+17-17=6b^3+17-17[/tex]
[tex]-x=6b^3[/tex]
Dividing both sides by -1, we get
[tex]x=-6b^3[/tex]
Hence, ? = [tex]-6b^3[/tex]
10x^3+40x^2+15x
------------------------------
5x
Answer:
Step-by-step explanation:
[tex]\dfrac{10x^3 + 40x^2 + 15x}{5x}\\ \dfrac{10x^3}{5x} +\dfrac{40x^2}{5x}+\dfrac{15x}{5x}[/tex]
2x^2 + 8x + 3 is your final answer.
HELP ASAP!!! IM BEING TIMED. Use synthetic division to test one potential root. Enter the numbers that complete the division problem.
Step-by-step explanation:
1 * (-5) = -5 a = -5
6 + (-5) = 1 b = 1
1 * (-5 ) = -5 c = -5
-7 + -5 = -12 d = -12
The divisor of the polynomial in the synthetic long division is linear factor
The correct values are;
a = -5c = -5b = 1d = -12Reason:
[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &a & c & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ b \hspace {0.25 cm} d \hspace {0.25 cm} 0[/tex]
The divisor in the division is (x - (-5)) = (x + 5)
By synthetic long division, we have;
Carry down the 1 representing the leading coefficient
[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ & & & \end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1[/tex]Multiply the 1 brought down by the zero value of x which is -5, and take the result into the second line of the division symbol
-5 × 1 = -5
[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &-5 & & \end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1[/tex]Add the coefficient 6 to -5, and bring down the result
[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &-5 & & \end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ \ 1[/tex]Repeat the above steps again to get;
-5 × 1 = -5
[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &-5 & -5 & \end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ \ 1 \hspace {0.3 cm} -12[/tex]-5 × (-12) = 60
[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &-5 & -5 & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ \ 1 \hspace {0.25 cm} -12 \hspace {0.25 cm} 0[/tex]By comparison to the given synthetic long division, [tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &a & c & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ b \hspace {0.25 cm} d \hspace {0.25 cm} 0[/tex], we have;
a = -5, c = -5, b = 1, and d = -12
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The variable z is directly proportional to x. When x is 3, z has the value 48. What is the value of z when x = 7?
Answer:
112
Step-by-step explanation:
Given z is directly proportional to x then the equation relating them is
z = kx ← k is the constant of proportionality
To find k use the condition x = 3 when z = 48
k = [tex]\frac{z}{x}[/tex] = [tex]\frac{48}{3}[/tex] = 16, thus
z = 16x ← equation of proportionality
When x = 7, then
z = 16 × 7 = 112
Two planes travel toward each other from cities that are about 450 km apart at rates of 240 km/hr and 210 km/hr. They started at the same time. In how many hours will they meet?
Answer:
1 hour.
Step-by-step explanation:
You have to do the total distance /total speed together.
You have to do this to ensure that you are counting how fast they are travelling together.
(450 km) / the sum of their speed (240+210)
450/ (240+210)
=450/ 450
=1
Answer: 1 Hour.
Answer:
t = 1 hour
Step-by-step explanation:
Oddly the distances add. Each plane will contribute a certain distance to make the 450 km. They will meet after the same number of hours have passed.
d = r * t
r1 = 240 km/hour
t1 = t
r2 = 210 km/hour
t2 = t
240*t + 210*t = 450 collect the terms on the left.
450t = 450 divide by 450
450t/450 = 450/450
t =1
After 1 hour they will meet.
The oblique pyramid has a square base. What is the volume of the pyramid? 2.5cm3 5cm3 6cm3 7.5cm3
Answer:
V = 5 cm³Step-by-step explanation:
The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - base area
H - height
In the base we have a square withe side s = 2cm
The formula of an area of a square with side s:
[tex]A=s^2[/tex]
Substitute:
[tex]A=2^2=4\ cm^2[/tex]
The height H = 3.75 cm.
Calculate the volume:
[tex]V=\dfrac{1}{3}(4)(3.75)=\dfrac{15}{3}=5\ cm^3[/tex]
Answer: C. 58 1/3 cm∧2
Just took quiz.
What are the solutions of the equation x^2=9
To solve this you must completely isolate x. This means that you have to get rid of the square from the x. To do this take the square root of both sides (square root is the opposite of squaring something and will cancel the square from the x)
√x² = √9
x = 3
and
x = -3
Check:
3² = 9
3*3 = 9
9 = 9
(-3)² = 9
-3 * -3 = 9
9 = 9
Hope this helped!
~Just a girl in love with Shawn Mendes
If p represents a digit and 4p/6p + 5/17 = 1, what digit does p represented?
Answer:
p=8
Step-by-step explanation:
We know that 'p' represents a digit.
We can say that:
x + 5/17 = 1
Solving for 'x' we have:
x = 1 -5/17
x = 12/17
Now, multiplying 'x' by 4, we have:
x = 48/68
Therefore, p=8
Three times a number added twice a smaller number is 4. Twice the smaller number less than twice the larger number is 6. Find the number
Answer:
x= -2/5 and y=13/5
Step-by-step explanation:
Lets assume that the larger number = x
And the smaller number = y
According to the given statement three times a number added twice a smaller number is 4, it means;
3x+2y=4 -------- equation 1
Now further twice the smaller number less than twice the larger number is 6,it means;
2y-2x=6 --------equation 2
Solve the equation 2.
2y=2x+6
y=2x+6/2
y=2(x+3)/2
y=x+3
Substitute the value of y=x+3 in the first equation.
3x+2y=4
3x+2(x+3)=4
3x+2x+6=4
Combine the like terms:
5x=4-6
5x=-2
x= -2/5
Put the value x= -2/5 in equation 2.
2y-2x=6
2y-2(-2/5)=6
2y+4/5=6
By taking L.C.M we get
10y+4/5=6
10y+4=6*5
10y+4=30
10y=30-4
10y=26
y=26/10
y=13/5
Hence x= -2/5 and y=13/5....
To find the numbers, we first solve for x and y using a system of equations. We find that x is 2 and y is -1. Thus, the larger number is 2 and the smaller number is -1.
Detailed Explanation is as follows:
Let the larger number be x and the smaller number be y. Based on the problem, we can set up the following system of equations:
3x + 2y = 4
2x - 2y = 6
Add the equations together to eliminate y.
3x + 2y + 2x - 2y = 4 + 6
5x = 10
x = 2
Now, Substitute x back into one of the original equations
Using the first equation:
3(2) + 2y = 4
6 + 2y = 4
2y = -2
y = -1
Therefore, the larger number is 2 and the smaller number is -1.
Hence the larger number is 2 and the smaller number is -1.
plz show that
[tex] \tan( \frac{\pi}{4} - \alpha ) \: \tan( \frac{\pi}{4} + \alpha ) = 1[/tex]
Solution:
The formula for tan(A+B) and tan(A-B) are:
[tex]tan(A+B) = \frac{tan(A)+tan(B)}{1-tan(A)tan(B)} \\\\tan(A-B) = \frac{tan(A)-tan(B)}{1+tan(A)tan(B)}[/tex]
The left hand side of the given expression is:
[tex]tan(\frac{\pi}{4}-\alpha ) tan(\frac{\pi}{4}+\alpha )[/tex]
Using the formula above and value of tan(π/4) = 1, we can expand this expression as:
[tex]tan(\frac{\pi}{4}-\alpha ) tan(\frac{\pi}{4}+\alpha )\\\\ = \frac{tan(\frac{\pi}{4} )-tan(\alpha)}{1+tan(\frac{\pi}{4} )tan(\alpha)} \times \frac{tan(\frac{\pi}{4} )+tan(\alpha)}{1-tan(\frac{\pi}{4} )tan(\alpha)}\\\\ = \frac{1-tan(\alpha)}{1+tan(\alpha)} \times \frac{1+tan(\alpha)}{1-tan(\alpha)}\\\\ = 1 \\\\ = R.H.S[/tex]
Thus, the left hand side is proved to be equal to right hand side.
Find the value of x in the picture
Answer: [tex]x=129\°[/tex]
Step-by-step explanation:
By definition, it is important to remember that:
[tex]Angle\ formed\ by\ two\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)[/tex])
You can observe in the figure that "x" is an Angle formed by two chords, therefore, you can find its value applying the formula.
Therefore, the value of "x" is this:
[tex]x=\frac{1}{2}(204\°+54\°)\\\\x=\frac{1}{2}(258\°)\\\\x=129\°[/tex]
For the parent function y=√x what effect does a value of k = -3 have on the graph?
Horizontal shift of 3 units to the right
Horizontal shift of 3 units to the left
Vertical shift of 3 units up
Vertical shift of 3 units down
Answer:
Vertical shift of 3 units down ⇒ last answer
Step-by-step explanation:
* Lets revise the translation of a function
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Lets solve the problem
∵ The parent function y = √x
∵ There is a translation by k = -3
- From the rules above k is for the vertical translation
∵ k = -3
- That means the parent function translated 3 units down
∴ The value of k = -3 makes the graph of the parent function translated
3 units down
- For more understand look to the attached graph
# y = √x ⇒ the red graph
# y = √x - 3 ⇒ the blue graph
to the nearest hundreth, what is the circumference of a circle with a radius of 7 units?
Answer:153.94
Step-by-step explanation:circumference is πr^2
π × 49 = 153.93804
Nearest hundredth count two digits after the decimal(to make an hundredth), then round off with the third number
1/4 x ≤ -3 solve for x
moving 4 to the other side x= 4 × -3 =-12
so x =-12
Answer:
x ≤ -12
Step-by-step explanation:
1/4 x ≤ -3
Multiply by 4 on both sides to get rid of the fraction coefficient.
x ≤ -12
This means x is x is equal to or less than -12
A right pyramid with a square base has a base edge length of 12 meters and slant height of 6 meters.
The apothem is meters.
The hypotenuse of ΔABC is the .
The height is meters.
The volume of the pyramid is cubic meters.
Answer:
Step-by-step explanation:
Square base of the base edge = 12 meters and slant height = 6√2 meters
Apothem of the right pyramid will be = AC
1). Now AC = [tex]\sqrt{AB^{2}-BC^{2}}[/tex]
AC = [tex]\sqrt{(6\sqrt{2})^{2}-(6)^{2}}[/tex]
= [tex]\sqrt{72-36}=\sqrt{36}[/tex]
= 6
Now Apothem = 6 meters
2). Hypotenuse of Δ ABC = AB = 6√2 meters
3). Height AC = 6 meters
4). Volume of the pyramid = [tex]\frac{1}{3}(\text{Area of the base})(\text{Apothem})[/tex]
Volume = [tex]\frac{1}{3}(12)^{2}(6)[/tex]
= 2×144
= 288 meter²
Correct responses:
The apothem is 6 metersThe hypotenuse of ΔABC is 6·√2 metersThe height is 6 meterThe volume of the pyramid is 288 cubic metersMethods used for the calculationsThe given dimensions of the right pyramid having a square base are;
Base edge length, l = 12 meters
Slant height = 6·√3
Required:
Length of the apothem.
Solution:
The apothem, a, is the line drawn from the middle of the polygon to the midpoint of a side.
Therefore;
The apothem of the square base = [tex]\dfrac{l}{2} [/tex] = [tex]\overline{BC}[/tex]
Which gives;
[tex]a = \dfrac{12}{2} = 6[/tex]
The apothem is 6 metersRequired:
The hypotenuse of triangle ΔABC
Solution:
The hypotenuse of ΔABC = The slant height of the square pyramid = 6·√2 meters
Therefore;
The hypotenuse of ΔABC = 6·√2 metersRequired:
The height of the pyramid
Solution:
The height of the pyramid = The length of the side [tex]\overline{AC}[/tex] in right triangle
ΔABC, therefore, by Pythagorean theorem, we have;
[tex]\overline{AC}^2[/tex] = [tex]\overline{AB}^2[/tex] - [tex]\overline{BC}^2[/tex]
Which gives;
[tex]\overline{AC}^2[/tex] = (6·√2)² - 6² = 6²·((√2)² - 1) = 6² × 1 = 6²
[tex]\overline{AC}[/tex] = √(6²) = 6
The height of the pyramid, h = [tex]\overline{AC}[/tex] = 6 metersRequired:
The volume of the pyramid.
Solution:
[tex]The \ volume \ of \ a \ pyramid \ is, \ V = \mathbf{\dfrac{1}{3} \times Base \ area \times Height}[/tex]
[tex]V = \dfrac{1}{3} \times A \times h [/tex]
The base area of the square pyramid, A = 12 m × 12 m = 144 m²
Therefore;
[tex]V = \dfrac{1}{3} \times 144\, m^2 \times 6 \, m = 288 \, m^2[/tex]
The volume of the pyramid is V = 288 cubic metersLearn more about the volume of solids here:
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Which of the following describes a compound event?
A. Tossing a coin and getting heads
B. Drawing the ace of hearts from a deck of cards
C. Rolling 2 on a die
D. Drawing an ace from a deck of cards and getting heads on a coin
toss
HELP PLEASE
Answer:
D. Drawing an ace from a deck of cards and getting heads on a coin
toss
Step-by-step explanation:
Drawing an ace from a deck of cards and getting heads on a coin
toss describes a compound event.
Answer:
D. Drawing an ace from a deck of cards and getting heads on a coin
toss.
Step-by-step explanation:
Compound event means being able to get more than one different outcome in any given time. This means that the result is not always the same. Most of the time, this consists of more than one event, and that the event has nothing to do with each other (independent compound events).
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which formula can be used to describe the sequence below 27,9,3
Answer:
[tex]a_n=27 \cdot (\frac{1}{3})^{n-1}[/tex].
Step-by-step explanation:
This is a geometric sequence that means there is a common ratio. That means there is a number you can multiply over and over to get the next term.
The first term is 27.
The second term is (1/3)(27)=9.
The third term is (1/3)(9)=3.
So the common ratio is 1/3.
That means you can keep multiplying by 1/3 to find the next term in the sequence.
The explicit form for a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.
We are given [tex]a_1=27[/tex] and [tex]r=\frac{1}{3}[/tex].
So the explicit form for the given sequence is [tex]a_n=27 \cdot (\frac{1}{3})^{n-1}[/tex].
Answer:
Its b on edge 2021
Step-by-step explanation:
just did it
Which points are a distance of 5 units from (2, 3) if ? (7, 3) (–1, –1) (0, 3) (2, 8) (−7, 6)
Answer:
(7, 3), (–1, –1) and (2, 8) are at a distance of units from (2, 3).
Step-by-step explanation:
We know that the formula of distance is given by:
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So substituting the given points points to check which points are at a distance of 5 units from [tex](2,3)[/tex].
1. (2, 3) and (7, 3):
[tex]\sqrt{(7-2)^2+(3-3)^2} =\sqrt{25} = 5[/tex]
2. (2, 3) and (–1, –1):
[tex]\sqrt{(-1-2)^2+(-1-3)^2} =\sqrt{25} = 5[/tex]
3. (2, 3) and (0, 3):
[tex]\sqrt{(0-2)^2+(3-3)^2} =\sqrt{4} = 2[/tex]
4. (2, 3) and (2, 8):
[tex]\sqrt{(2-2)^2+(8-3)^2} =\sqrt{25} = 5[/tex]
5. (2, 3) and (-7, 6):
[tex]\sqrt{(-7-2)^2+(6-3)^2} =\sqrt{90} =9.5[/tex]
Answer:
Step-by-step explanation:
The correct answer are A B and D
I just took the test
I need to find q, r, s, t
The function is g(x)=2x^2-8
Answer:
q=0
r=2
s=3
t=-3
Step-by-step explanation:
q represents the value we should get from evaluating d(-8).
[tex]d(x)=-\sqrt{\frac{1}{2}x+4}[/tex]
To find d(-8) we use this function here labeled d and replace x with -8:
[tex]d(-8)=-\sqrt{\frac{1}{2}(-8)+4}[/tex]
[tex]d(-8)=-\sqrt{-4+4}[/tex]
[tex]d(-8)=-\sqrt{0}[/tex]
[tex]d(-8)=0[/tex]
So q is 0 since d(-8)=0.
r represents the value we should get from evaluating f(0).
[tex]f(x)=\sqrt{\frac{1}{2}x+4}[/tex]
To find f(0) we use this function labeled f and repalce x with 0:
[tex]f(0)=\sqrt{\frac{1}{2}(0)+4}[/tex]
[tex]f(0)=\sqrt{0+4}[/tex]
[tex]f(0)=\sqrt{4}[/tex]
[tex]f(0)=2[/tex]
So r is 2 since f(0)=2.
s represents the value we should get from evaluating f(10).
[tex]f(x)=\sqrt{\frac{1}{2}x+4}[/tex]
To find f(10) we use this function labeled f and replace x with 10:
[tex]f(10)=\sqrt{\frac{1}{2}(10)+4}[/tex]
[tex]f(10)=\sqrt{5+4}[/tex]
[tex]f(10)=\sqrt{9}[/tex]
[tex]f(10)=3[/tex]
So s is 3 since f(10)=3.
t represents the value we should get from evaluating d(10).
[tex]d(x)=-\sqrt{\frac{1}{2}x+4}[/tex]
To find d(10) we use the function labeled d and replace x with 10:
[tex]d(10)=-\sqrt{\frac{1}{2}(10)+4}[/tex]
[tex]d(10)=-\sqrt{5+4}[/tex]
[tex]d(10)=-\sqrt{9}[/tex]
[tex]d(10)=-3[/tex]
So t is -3 since d(10)=-3
q=0
r=2
s=3
t=-3
Evaluate |c^2 +b^2|, given a=5, b=-3, and c=-2.
2
6
10
13
Answer:
13Step-by-step explanation:
|a| = a for a ≥ 0
|a| = -a for a < 0
============================================
|c² + b²|
Put b = -3 and c = -2 to the expression:
|(-2)² + (-3)²| = |4 + 9| = |13| = 13
Nathan has 102 solid-colored disks that are red.
blue, and green. He lines them up on the floor
and finds that there are 3 more red disks than blue
and 6 more blue disks than green. How many red
disks are there?
Answer:
blue = 35
green = 29
red = 38
Step-by-step explanation:
Let r = red
Let g = green
let b = blue
r + g + b = 102
r = b + 3
b = g + 6 Subtract 6 from both sides of the equation
b - 6 = g
===================
substitute for red and green
(b + 3) + b + b - 6 = 102
b + 3 + b + b - 6 = 102
Combine like terms
3b - 3 = 102
Add 3 to both sides
3b - 3 + 3 = 102 + 3
3b = 105
Divide by 3
3b/3 = 105/3
b = 35
======================
r = b + 3
r = 35 + 3
r = 38
=======================
g = b - 6
g = 35 - 6
g = 29
========================
Answer:
red=35 green=29 blue=38
Step-by-step explanation:
Can you please mildly explain this with the answer.
[tex]\bf \begin{cases} f(x)=&5x-1\\ f(-3)=&5(-3)-1\\ f(-3)=&-15-1\\ f(-3)=&-16 \end{cases}\qquad \begin{cases} g(x)=&2x^2+1\\ g(-3)=&2(-3)^2+1\\ g(-3)=&2(-3)(-3)+1\\ g(-3)=&2(9)+1\\ g(-3)=&18+1\\ g(-3)=&19 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (f\times g)(-3)\implies f(-3)\times g(-3)\implies (-16)(19)\implies -304[/tex]